Mathematics Testlet Blueprint
Numbers and Operations – Fractions
Purpose of Assessment: To collect evidence of student understanding to inform instruction.
Content Area/Domain: Numbers and Operations – Fractions
| Grade: 4
Time Needed for Administration: 20 minutes
| Total Score: 10 points
Materials Needed: Student Test Form and Scoring Guide
Item Specifications:
Cluster
Target Standards
(Key concepts/skills to be assessed)
Build fractions from unit fractions by applying and
extending previous understandings of operations on
whole numbers.
Build fractions
from unit
fractions
by applying
and extending
previous
understandings
of operations
on whole
numbers.
Depth of
# of
Item
Item Type
Knowledge (MC/SA/CR*) Items Position
(DOK)
2
SA
1
4
3
CR
1
7
Understand a fraction a/b with a > 1 as a sum of
fractions 1/b.
1
MC
1
1
Understand addition and subtraction of fractions as
joining and separating parts referring to the same
whole.
1
MC
1
3
Add and subtract mixed numbers with like
denominators, e.g., by replacing each mixed
number with an equivalent fraction, and/or by
using properties of operations and the relationship
between addition and subtraction.
2
SA
1
5
Solve word problems involving addition and
subtraction of fractions referring to the same whole
and having like denominators, e.g., by using visual
fraction models and equations to represent the
problem.
2
SA
1
6
Solve word problems involving multiplication of
a fraction by a whole number, e.g., by using visual
fraction models and equations to represent the
problem.
2
MC
1
2
*MC = Multiple Choice, SA = Short Answer, CR = Constructed Response
A1
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CCAP2004.3
Student Learning Targets
Grade 4 Mathematics Testlet – Numbers and Operations – Fractions
1. I can build fractions from unit fractions.
2. I understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
3. I can add and subtract mixed numbers using equivalent fractions.
4. I can solve word problems involving addition and subtraction of fractions referring to
the same whole and having like denominators.
5. I can solve word problems involving multiplication of a fraction by a whole number.
A2
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CCAP2004.3
Student Test Form
Grade 4 Mathematics Testlet – Numbers and Operations – Fractions
STUDENT NAME:
TEACHER NAME:
DATE:
For each question, choose the correct answer. Then completely fill in the circle for the answer
you chose.
107899A Multiple Choice A In Development
104309A Multiple Choice C Common
1
2. Lisa had 2 8 bags of apples. She used
5
1 of the bags of apples to make pies.
1. Jason bought this pizza.
8
Which model shows how to find the
number of bags of apples she has left?
Jason ate 2 of the pizza. What part of
3
the pizza is left?
A
X X X X
X X X X
B
X X X
X X
C
X X X X
X X X X
X X X X
X X X
D
X X X X
X X X X
X X X
X X
1
A 6
X X X
X X
1
B 5
1
C 3
1
D 2
1
©2012 Measured Progress. All rights reserved.
Go On
Grade 4 Mathematics Testlet – Numbers and Operations – Fractions
107893A Multiple Choice B In Development
For each short-answer question, show your
thinking in the box labeled “Show your work
here” and write your answer in the box
labeled “Answer.”
3. Amy cut a piece of fabric into 10 pieces
9
that are all the same size. She used 10
of the fabric for a project.
105519A Short Answer Operational Matrix
4. You may use this number line to help
you answer the question.
0
Which number sentence is true?
2
8
9
A 10 1 10 5 10
3
6
6
5
1
–
2
3
–
4
9
the afternoon. Write a fraction that tells
9
how long, in hours, Lainey practiced her
trumpet that day.
9
D 5 1 5 5 10
Show your work here:
Answer:
2
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1
1
1
hour
in
the
morning
and
hour in
2
4
C 4 1 6 5 10
4
4
Lainey practiced her trumpet for
B 10 1 10 5 10
3
1
–
Go On
Grade 4 Mathematics Testlet – Numbers and Operations – Fractions
105517A Short Answer Operational Matrix EQ
105518A Short Answer Operational Matrix EQ
3
1
5. James ran 1 4 miles. Raul ran 1 miles.
4
6. You may use this number line to help
you answer the question.
Write a fraction that tells how much
farther, in miles, James ran than Raul.
1
—
0 10
1
–
2
1
Show your work here:
Ramona has red and blue bracelets.
• 3 are red
10
4
• 10 are blue
Write a fraction that tells what part of
Ramona’s bracelets are either red or
blue.
Answer:
Show your work here:
Answer:
3
©2012 Measured Progress. All rights reserved.
Go On
Grade 4 Mathematics Testlet – Numbers and Operations – Fractions
For this question, write your answer to each part in the box provided. Be sure to show your
work or explain your answer.
103284A Constructed Response Field Test / Pilot
7. This picture shows Greg’s garden.
1
Greg planted pumpkins in 12 of the garden.
a. How many of the squares represent the space planted with pumpkins?
Greg planted squash in
7
of the garden.
12
b. How many of the squares represent the space planted with squash?
The remainder of the garden will be planted with tomatoes.
c. What fraction of the garden will be planted with tomatoes? Show your work or explain
how you know.
4
©2012 Measured Progress. All rights reserved.
Scoring Guide
Numbers and Operations – Fractions
Multiple-Choice Items
CCSS Alignment
CCSS Alignment
CLUSTER: Build fractions from unit fractions by applying
and extending previous understandings of operations on
whole numbers.
CLUSTER: Build fractions from unit fractions by applying
and extending previous understandings of operations on
whole numbers.
STANDARD: Understand a fraction a/b with a > 1 as a sum of
fractions 1/b.
STANDARD: Solve word problems involving multiplication
of a fraction by a whole number, e.g., by using visual
fraction models and equations to represent the problem.
DOK: 1
DOK: 2
1. Jason bought this pizza.
1
2. Lisa had 2 8 bags of apples. She used
5
1 of the bags of apples to make pies.
8
Which model shows how to find the
number of bags of apples she has left?
Jason ate 2 of the pizza. What part of
3
the pizza is left?
1
A 6
1
B 5
1
C 3
1
D 2
Distractor Rationales
A
B
C
D
Sees 6 pieces
Adds numerator and denominator and uses sum
as the denominator of the answer
Key
Marks off 2/3 of pizza, sees 2 pieces left and
4 pieces eaten, and makes a fraction 2/4 = 1/2
A
X X X X
X X X X
X X X
X X
B
X X X
X X
C
X X X X
X X X X
X X X X
X X X
D
X X X X
X X X X
X X X
X X
Distractor Rationales
A
B
C
D
Key
Only subtracts fraction part of 1 5/8
Interprets 2 1/8 as 21/8 and 1 5/8 as 15/8
Interprets 2 1/8 as 21/8
B1
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Measured Progress COMMON CORE and its logo are trademarks of Measured Progress, Inc.
CCAP2004.3
Scoring Guide
Short-Answer Items
CCSS Alignment
CCSS Alignment
CLUSTER: Build fractions from unit fractions by applying
and extending previous understandings of operations on
whole numbers.
CLUSTER: Build fractions from unit fractions by applying
and extending previous understandings of operations on
whole numbers.
STANDARD: Understand addition and subtraction of
fractions as joining and separating parts referring to the
same whole.
STANDARD: Build fractions from unit fractions by applying
and extending previous understandings of operations on
whole numbers.
DOK: 1
DOK: 2
3. Amy cut a piece of fabric into 10 pieces
9
4. You may use this number line to help
you answer the question.
that are all the same size. She used 10
of the fabric for a project.
1
–
0
1
–
4
2
3
–
1
4
Lainey practiced her trumpet for
1
1
hour
in
the
morning
and
hour in
2
4
Which number sentence is true?
2
8
9
A 10 1 10 5 10
3
6
9
B 10 1 10 5 10
3
6
9
C 4 1 6 5 10
4
5
how long, in hours, Lainey practiced her
trumpet that day.
Short-Answer Rubric
SCORE
Distractor Rationales
DESCRIPTION
3
(hour) or equivalent
4
1
Answer:
0
Response is incorrect or contains some
correct work that is irrelevant to the skill or
concept being measured.
9
D 5 1 5 5 10
A
B
C
D
the afternoon. Write a fraction that tells
Blank
No response.
Numerators add up to 10
Key
Adds numerators and denominators
Adds numerators and denominators
B2
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CCAP2004.3
Scoring Guide
CCSS Alignment
CCSS Alignment
CLUSTER: Build fractions from unit fractions by applying
CLUSTER: Build fractions from unit fractions by applying
and extending previous understandings of operations on
whole numbers.
and extending previous understandings of operations on
whole numbers.
STANDARD: Add and subtract mixed numbers with like
denominators, e.g., by replacing each mixed number
with an equivalent fraction, and/or by using properties
of operations and the relationship between addition and
subtraction.
STANDARD: Solve word problems involving addition and
subtraction of fractions referring to the same whole and
having like denominators, e.g., by using visual fraction
models and equations to represent the problem.
DOK: 2
DOK: 2
3
1
5. James ran 1 4 miles. Raul ran 1 miles.
4
6. You may use this number line to help
you answer the question.
Write a fraction that tells how much
farther, in miles, James ran than Raul.
Short-Answer Rubric
SCORE
DESCRIPTION
1
(mile) or equivalent
2
1
Answer:
0
Response is incorrect or contains some
correct work that is irrelevant to the skill or
concept being measured.
Blank
1
—
0 10
1
–
2
1
Ramona has red and blue bracelets.
• 3 are red
10
4
• 10 are blue
Write a fraction that tells what part of
Ramona’s bracelets are either red or
blue.
No response.
Short-Answer Rubric
SCORE
DESCRIPTION
7
or equivalent
10
1
Answer:
0
Response is incorrect or contains some
correct work that is irrelevant to the skill or
concept being measured.
Blank
No response.
B3
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CCAP2004.3
Scoring Guide
Constructed-Response Item
CCSS Alignment
CLUSTER: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
STANDARD: Build fractions from unit fractions by applying and extending previous understandings of operations on whole
numbers.
DOK: 3
7. This picture shows Greg’s garden.
1
Greg planted pumpkins in 12 of the garden.
a. How many of the squares represent the space planted with pumpkins?
Greg planted squash in
7
of the garden.
12
b. How many of the squares represent the space planted with squash?
The remainder of the garden will be planted with tomatoes.
c. What fraction of the garden will be planted with tomatoes? Show your work or explain
how you know.
Constructed-Response Rubric
SCORE
DESCRIPTION
Constructed-Response Scoring Notes:
Training Notes
4
4 points
Part a. 1 point
Part b. 1 point
for correct answer, 3 (squares)
for correct answer, 21 (squares)
3
3 points
Part c. 2 points
for correct answer,
2
2 points
1
1 point
0
Response is incorrect or contains some
correct work that is irrelevant to the skill or
concept being measured.
Blank
No response.
OR
1 point
4
or equivalent,
12
with sufficient explanation or work
shown to indicate correct strategy
for correct answer with insufficient or
no explanation or work shown
or
for sufficient strategy with incorrect or
no answer
Sample Response
1
12 1
=
. 24 squares have been planted, so 12 are left.
c.
3
36 3
B4
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CCAP2004.3
Formative Tools
The COMMON CORE Testlets are intended to support classroom formative assessment practices. The following
optional tools are offered to help engage students in the assessment process. These tools can also assist teachers in
using the evidence collected from the Testlets to inform instructional next steps.
Tools for Students:
1. Learning Targets: Serve as a test blueprint for students. The learning targets specify the learning expectations
of the Common Core standards being addressed within each Testlet. Learning targets can be shared with
students prior to administering the Testlet and can be used with a self-assessment pre- or post-administration.
2. Learning Target Self-Assessment: A template for students to review the learning targets, identify their current
level of understanding, and monitor their progress.
3. Student Item Analysis and Feedback: A form for students to analyze which items were correct and incorrect,
and what they still need help learning. This form provides students with an opportunity to reflect on their own
performance and identify learning goals.
Tools for Teachers:
1. Response Review Form: A guide for reviewing student responses and recording evidence about student
response patterns regarding specific distractors and skill areas that need more instructional attention.
2. Constructed-Response Task Review: A guide for reviewing student work and recording evidence of student
understanding. The evidence collected through analyzing student responses and the accompanying rubrics can
be used as formative feedback.
3. Formative Feedback: A template for recording how students are meeting the learning expectations and
suggestions for next steps to move learning forward. The formative feedback form can be used between teachers
and students, or peer to peer.
C1
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Measured Progress COMMON CORE and its logo are trademarks of Measured Progress, Inc.
CCAP2000.Math
Formative Tools
Learning Target Self-Assessment
Self-assess each target with the following code:
G I can do this.
Y I am working toward learning this.
R I am just beginning this.
Target:
Name:
Unit:
Grade Level:
G
Y
R
G
Y
1.
Pre
Post
2.
Pre
Post
3.
Pre
Post
4.
Pre
Post
5.
Pre
Post
R
C2
©2012 Measured Progress. All rights reserved. | Web: measuredprogress.org
CCAP2000.Math
Formative Tools
Student Analysis and Feedback
Student Name:
teacher name:
date:
1.
To help keep track of your own learning and provide some instructional feedback for your teacher, look back at
the questions, review your responses, and check what you understand or what you still don’t understand.
Question Analysis
question #
i understand 
i still don’t understand 
1
o
o
2
o
o
3
o
o
4
o
o
5
o
o
6
o
o
Totals
2.Feedback for Me and My Teacher: Looking at your question analysis, your teacher feedback, and your
self-assessment of learning targets, what do you still need help learning?
I still need help learning:
My Learning Goals:
_______________________________________________________________________________________________________________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________________________________________________________________________________________________________
C3
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CCAP2000.Math
Formative Tools
Formative Tools
Response Review
Student Name:
teacher name:
date:
Multiple-Choice and Short-Answer Item Review
1.
Use the scoring guide to analyze student responses and record correct and incorrect responses in the table below.
As you review student responses, review the distractor rationales and note the target standards/concepts/skills
being assessed with each item.
Item Analysis
Distractor Rationale Review Notes
Item #
Correct 
Incorrect 
Item #
1
o
o
1
2
o
o
2
3
o
o
3
4
o
o
4
5
o
o
5
6
o
o
6
Totals
2.Analysis: Based on this evidence of student understanding, which specific areas seem to need more instructional
attention?
C4
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CCAP2000.Math
Formative Tools
Constructed-Response Task Review Guide
Constructed-Response Task
1.
Review Student Work: Use the rubric and scoring notes to look for evidence of the student meeting expectations.
What do you notice about the student’s work? How has the student demonstrated understanding?
What misconceptions are evident?
2.
List evidence of student understanding and/or misconceptions:
3.Using the rubric, determine the number of score points earned at this time (optional):
= # of score points earned for the constructed-response task.
4.Use Results to Inform Teaching and Learning:
ƒƒ
Evidence Review: How can this student evidence be used to inform instructional next steps?
ƒƒ
Feedback for Student: How can the student move forward with his or her learning?
Provide some descriptive feedback to help the student set learning goals and improve his or her
understanding and performance.
C5
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CCAP2000.Math
Formative Tools
Formative Feedback
Student Name:____________________________________________
Areas of strength and
evidence of mastery
within this set of targets:
Areas that require additional
learning or more focus
within this set of targets:
Other comments:
C6
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CCAP2000.Math